The flow due to a rough rotating disk

Miklavčič, Milan; Wang, C. Y.

doi:10.1007/s00033-003-2096-6

Cited by 123 publications

(87 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In particular, our numerical values agree exactly with those appearing in Table 1 of Miklavčič and Wang. 23 For the case of anisotropic roughness with concentric grooves, increasing η results in a slight thickening of the boundary layer and a reduction in the radial jet, as evident in Figure 1 increased. In contrast, for the case of radial grooves, there is a slight thinning of the boundary layer and an increase in the radial jet, as seen in Figure 1(b).…”

Section: The Steady Flowmentioning

confidence: 82%

“…23 The disk is considered to be infinite in diameter and rotating about its axis of symmetry at a constant rotation rate Ω. It is natural to consider this geometry in a cylindrical polar coordinate system (r * , θ, z * ) in which the governing Navier-Stokes equations are well known.…”

Section: The Steady Flowmentioning

confidence: 99%

“…They were developed by Miklavčič and Wang 23 and Yoon et al 24 and are henceforth referred to as the MW and YHP models, respectively. Both models show how successively increasing roughness levels lead to deviations from the classic similarity solution for the smooth disk due to von Kármán.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The effect of anisotropic and isotropic roughness on the convective stability of the rotating disk boundary layer

et al. 2015

View full text Add to dashboard Cite

A theoretical study investigating the effects of both anisotropic and isotropic surface roughness on the convective stability of the boundary-layer flow over a rotating disk is described. Surface roughness is modelled using a partial-slip approach, which yields steady-flow profiles for the relevant velocity components of the boundary-layer flow which are a departure from the classic von Kármán solution for a smooth disk. These are then subjected to a linear stability analysis to reveal how roughness affects the stability characteristics of the inviscid Type I (or cross-flow) instability and the viscous Type II instability that arise in the rotating disk boundary layer. Stationary modes are studied and both anisotropic (concentric grooves and radial grooves) and isotropic (general) roughness are shown to have a stabilizing effect on the Type I instability. For the viscous Type II instability, it was found that a disk with concentric grooves has a strongly destabilizing effect, whereas a disk with radial grooves or general isotropic roughness has a stabilizing effect on this mode. In order to extract possible underlying physical mechanisms behind the effects of roughness, and in order to reconfirm the results of the linear stability analysis, an integral energy equation for three-dimensional disturbances to the undisturbed three-dimensional boundary-layer flow is used. For anisotropic roughness, the stabilizing effect on the Type I mode is brought about by reductions in energy production in the boundary layer, whilst the destabilizing effect of concentric grooves on the Type II mode results from a reduction in energy dissipation. For isotropic roughness, both modes are stabilized by combinations of reduced energy production and increased dissipation.

show abstract

Section: The Steady Flowmentioning

confidence: 82%

Section: The Steady Flowmentioning

confidence: 99%

See 1 more Smart Citation

The effect of anisotropic and isotropic roughness on the convective stability of the rotating disk boundary layer

et al. 2015

View full text Add to dashboard Cite

show abstract

“…In order to establish whether the predicted roughness effects arose as an artefact of the particular modelling approach of Ref. [2] we have attempted to reproduce them by means of an alternative, fundamentally different theoretical approach for the implementation of surface roughness. Here we summarize the results obtained from this alternative analysis and compare them to our original set of data from Ref.…”

Section: Introductionmentioning

confidence: 99%

On the stability of von Kármán rotating-disk boundary layers with radial anisotropic surface roughness

et al. 2016

View full text Add to dashboard Cite

We summarise results of a theoretical study investigating the distinct convective instability properties of steady boundary-layer flow over rough rotating disks. A generic roughness pattern of concentric circles with sinusoidal surface undulations in the radial direction is considered. The goal is to compare predictions obtained by means of two alternative, and fundamentally different, modelling approaches for surface roughness for the first time. The motivating rationale being to identify commonalities and isolate results that might potentially represent artefacts associated with the particular methodologies underlying one of the two modelling approaches.The most significant result of practical relevance obtained is that both approaches predict overall stabilising effects on the Type I instability mode of rotating disk flow. This mode leads to transition of the rotating-disk boundary layer and, more generally, the transition of boundary-layers with a cross-flow profile. Stabilisation of the Type 1 mode means that it may be possible to exploit surface roughness for laminar-flow control in boundary layers with a cross-flow component. However, we also find differences between the two sets of model predictions, some subtle and some substantial. These will represent criteria for establishing which of the two alternative approaches is more suitable to correctly describe experimental data when these become available.

show abstract

“…A substantial reduction in torque then occurred as a result of surface slip. Miklavcic and Wang (2004) further revisited the problem of Sparrow et al (Sparrow et al, 1971) and pointed out that the slip flow boundary conditions could also be used for slightly rarefied gases or for flow over grooved surfaces. Arikoglu and Ozkol (2006) studied MHD slip flow over a rotating disk with heat transfer.…”

Section: Introductionmentioning

confidence: 99%

Transient Hydromagnetic Forced Convective Heat Transfer Slip Flow Due to a Porous Rotating Disk with Variable Fluid Properties

Alam

Poddar²,

Rahman³

et al. 2015

AJHMT

View full text Add to dashboard Cite

In this paper we have studied the problem of an unsteady hydromagnetic forced convective heat transfer slip flow over a porous rotating disk taking into account the temperature dependent density, viscosity and thermal conductivity. The governing non-linear partial differential equations of the flow are transformed into a set of non-linear ordinary differential equations using similarity transformations. The resulting nondimensional equations have been solved numerically by applying Nachtsheim-Swigert shooting iteration technique along with sixth-order Runge-Kutta iteration scheme. Comparison with previously published work for the steady case of the problem is performed and the results are found to be in very good agreement. The results of the numerical solution are presented graphically in the form of velocity (i.e. radial, tangential as well as inward axial), temperature profiles and variable Prandtl number for various values of the model parameters. The corresponding skin friction coefficients (i.e. radial and tangential) and the rate of heat transfer coefficient (i.e. Nusselt number) are also calculated and tabulated. The obtained numerical results show that when modeling a thermal boundary layer with temperature dependent fluid properties, consideration of Prandtl number as constant within the boundary layer produces unrealistic results. Therefore, it must be treated as variable throughout the boundary layer. Results also show that the slip factor significantly controls the flow and heat transfer characteristics.

show abstract

The flow due to a rough rotating disk

Cited by 123 publications

References 13 publications

The effect of anisotropic and isotropic roughness on the convective stability of the rotating disk boundary layer

The effect of anisotropic and isotropic roughness on the convective stability of the rotating disk boundary layer

On the stability of von Kármán rotating-disk boundary layers with radial anisotropic surface roughness

Transient Hydromagnetic Forced Convective Heat Transfer Slip Flow Due to a Porous Rotating Disk with Variable Fluid Properties

Contact Info

Product

Resources

About